An adaptiveh-r boundary element algorithm for the laplace equation

A novel formulation of elastic multi-asperity contacts based on the boundary element method (BEM) is presented for the first time, in which the influence coefficients are numerically calculated using a finite element method (FEM). The main advantage of computing the influence coefficients in this manner is that it makes it also possible to consider an arbitrary load direction and multilayer systems of different mechanical properties in each layer. Furthermore, any form of anisotropy can be modelled too, where Green's functions either become very complicated or are not available at all. The rest of the contact analysis is then performed applying a custom-developed boundary element algorithm. The scheme was tested by considering the frictionless contact between a flat surface and a sphere. The obtained results are in good agreement with the analytical solution known for a Hertzian contact. Applied to either a frictionless or a frictional contact between real surfaces of different samples, our FEM-BEM method has shown that the composite roughness of surfaces in contact uniquely determines the contact pressure distribution.

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Numerical solution of the generalized Laplace equation by coupling the boundary element method and the perturbation method

Applied Mathematical Modelling ◽

10.1016/0307-904x(86)90057-0 ◽

1986 ◽

Vol 10 (4) ◽

pp. 266-270 ◽

Cited By ~ 9

Author(s):

R. Rangogni

Keyword(s):

Boundary Element Method ◽

Perturbation Method ◽

Numerical Solution ◽

Boundary Element ◽

Laplace Equation ◽

Generalized Laplace Equation ◽

Element Method

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Boundary Element Algorithm for Nonlinear Modeling and Simulation of Three-Temperature Anisotropic Generalized Micropolar Piezothermoelasticity with Memory-Dependent Derivative

International Journal of Applied Mechanics ◽

10.1142/s1758825120500271 ◽

2020 ◽

Vol 12 (03) ◽

pp. 2050027 ◽

Cited By ~ 2

Author(s):

Mohamed Abdelsabour Fahmy

Keyword(s):

Boundary Element ◽

Smart Materials ◽

Nonlinear Modeling ◽

Computation Time ◽

Industrial Applications ◽

Numerical Results ◽

Element Formulation ◽

Adaptive Smoothing ◽

Nonlinear Properties ◽

Element Algorithm

The main aim of this paper is to introduce a new memory-dependent derivative theory to contribute for increasing development of technological and industrial applications of anisotropic smart materials. This theory is called three-temperature anisotropic generalized micropolar piezothermoelasticity. The governing equations of the proposed theory are very difficult to solve analytically because of material anisotropy and its nonlinear properties. Therefore, we propose a new boundary element formulation for solving such equations. The efficiency of our proposed technique has been developed by using an adaptive smoothing and prolongation algebraic multigrid (aSP-AMG) preconditioner to reduce the computation time. The numerical results are presented highlighting the effects of the kernel function and time delay on the temperature and displacements. The numerical results also verify the validity and accuracy of the proposed methodology. It can be concluded from the numerical results of our current complex and general study that some well-known uncoupled, coupled and generalized theories of anisotropic micropolar piezothermoelasticity can be connected with the three-temperature radiative heat conduction to characterize the deformation of anisotropicmicropolar piezothermoelasticstructures in the context of memory-dependent derivative.

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Boundary Element Algorithm for Modeling and Simulation of Dual-Phase Lag Bioheat Transfer and Biomechanics of Anisotropic Soft Tissues

International Journal of Applied Mechanics ◽

10.1142/s1758825118501089 ◽

2018 ◽

Vol 10 (10) ◽

pp. 1850108 ◽

Cited By ~ 21

Author(s):

Mohamed Abdelsabour Fahmy

Keyword(s):

Boundary Element ◽

Soft Tissues ◽

Bioheat Transfer ◽

Phase Lag ◽

Dual Phase ◽

Lu Factorization ◽

Governing Equations ◽

Complex Shapes ◽

Incomplete Lu Factorization ◽

Element Algorithm

The main aim of this paper is to propose a new boundary element algorithm for describing thermomechanical interactions in anisotropic soft tissues. The governing equations are studied based on the dual-phase lag bioheat transfer and Biot’s theory. Due to the advantages of convolution quadrature boundary element method (CQBEM), such as low CPU usage, low memory usage and suitability for treatment of soft tissues that have complex shapes, it is a versatile and powerful method for modeling of bioheat distribution in anisotropic soft tissues and the related deformation. The resulting linear systems for bioheat and mechanical equations are solved by Transpose-free quasi-minimal residual (TFQMR) solver with a dual-threshold incomplete LU factorization technique (ILUT) preconditioner that reduces the iterations number and total CPU time. Numerical results demonstrate the validity, efficiency and accuracy of the proposed algorithm and technique.

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